In this sense it means that the business has to be well-organized, well run without waste and profitable. I can't tell you the origin for sure, but I'd guess it refers to a successful warrior: LEAN = fit, in good shape, not fat, and MEAN = aggressive, uncompromising.

A lean business or governing body is one that waste little money on people or systems/methods that are not productive. It has done away with as many wasteful / nonproductive elements as possible. Then, those people and systems that are productive are made as productive as possible. Mean = aggressive. The people and systems left are streamlined and meant to be do their jobs with the intention to be as: heartless = aggressive = out for gain = mean = productive = result oriented as possible.

"Lean and mean" describes someone, or some animal, (such as a bull dog), that is strong and powerful, that does not have a lot of fat and certainly is not lazy or sluggish. A business or company that is "lean and mean" would be an aggressive business that is out to make money, be profitable and climb to success. The employees would have to be their best, and help the company do better than its competition. To be this successful, the President of the company, or the "boss" will make sure the company employees are focused on their core activities and do not waste time doing other side activities that do not pertain to the goals of the company.